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Popular Calculus Problems

integral from 0 to pi^2 of sin(sqrt(x))	\int\:_{0}^{π^{2}}\sin(\sqrt{x})dx
derivative of 3x^{1/3}-5x^{4/3}	derivative\:3x^{\frac{1}{3}}-5x^{\frac{4}{3}}
integral of (sin^7(5x))/(cos^4(5x))	\int\:\frac{\sin^{7}(5x)}{\cos^{4}(5x)}dx
integral of tarcsec(t)	\int\:t\arcsec(t)dt
slope of (3,-3),(1,-1)	slope\:(3,-3),(1,-1)
tangent of f(x)=(1+2x)^{11},(0,1)	tangent\:f(x)=(1+2x)^{11},(0,1)
integral of sin(x)+sin(x)cos(x)	\int\:\sin(x)+\sin(x)\cos(x)dx
derivative of (t+e^t)(3-sqrt(t))	derivative\:(t+e^{t})(3-\sqrt{t})
derivative of (2x^2-1/(xsqrt(1+x^2)))	\frac{d}{dx}(\frac{2x^{2}-1}{x\sqrt{1+x^{2}}})
integral of (x^2)/(x-4)	\int\:\frac{x^{2}}{x-4}dx
derivative of 5	derivative\:5
(dy)/(dx)+6(tan(6x))y=2*cos(6x)	\frac{dy}{dx}+6\cdot\:(\tan(6x))\cdot\:y=2\cdot\:\cos(6x)
integral of (33x^2)/(sqrt(x^2-4))	\int\:\frac{33x^{2}}{\sqrt{x^{2}-4}}dx
integral from 0 to pi of xcos^2(x)	\int\:_{0}^{π}x\cos^{2}(x)dx
limit as x approaches 0 of (1-7x)^{1/x}	\lim\:_{x\to\:0}((1-7x)^{\frac{1}{x}})
integral of ((x^3-4x))/((x^2+1)^2)	\int\:\frac{(x^{3}-4x)}{(x^{2}+1)^{2}}dx
integral of 7x^4-5x^3+4x^2+C	\int\:7x^{4}-5x^{3}+4x^{2}+Cdx
limit as x approaches infinity+of 1/x	\lim\:_{x\to\:\infty\:+}(\frac{1}{x})
integral of 1/6 sec(x)tan(x)	\int\:\frac{1}{6}\sec(x)\tan(x)dx
derivative of (a-b/x ^2)	\frac{d}{dx}((a-\frac{b}{x})^{2})
sum from n=1 to infinity of 2/(n*(n+1))	\sum\:_{n=1}^{\infty\:}\frac{2}{n\cdot\:(n+1)}
derivative of g(x)=(4x^3+6x^2)^5	derivative\:g(x)=(4x^{3}+6x^{2})^{5}
d/(dθ)(2sin^2(θ))	\frac{d}{dθ}(2\sin^{2}(θ))
derivative of (ax-b(cx^2))	\frac{d}{dx}((ax-b)(cx^{2}))
integral of sin(ln(9x))	\int\:\sin(\ln(9x))dx
(dy)/(dx)+2y=5	\frac{dy}{dx}+2y=5
taylor xe^{2x}	taylor\:xe^{2x}
d/(dt)(cos(6t))	\frac{d}{dt}(\cos(6t))
limit as x approaches 0 of x(cot(x))	\lim\:_{x\to\:0}(x(\cot(x)))
limit as x approaches 3 of 2x-4	\lim\:_{x\to\:3}(2x-4)
integral of xsec(x^2)	\int\:x\sec(x^{2})dx
integral of ((x-3)^3)/(x^2-9)	\int\:\frac{(x-3)^{3}}{x^{2}-9}dx
limit as x approaches 4-of 8-2x	\lim\:_{x\to\:4-}(8-2x)
integral of pi(x+2)^2	\int\:π(x+2)^{2}dx
limit as x approaches 2 of-2	\lim\:_{x\to\:2}(-2)
(dx)/(dt)=xsin(t),x(0)=1	\frac{dx}{dt}=x\sin(t),x(0)=1
integral of 6tan(x)sec^3(x)	\int\:6\tan(x)\sec^{3}(x)dx
f(x)=8cos(x)	f(x)=8\cos(x)
integral of e^{-x^8}	\int\:e^{-x^{8}}dx
area y=x^2-2x,y=x	area\:y=x^{2}-2x,y=x
sum from n=1 to infinity of n^{(-2/3)}	\sum\:_{n=1}^{\infty\:}n^{(-\frac{2}{3})}
derivative of sqrt(x-2)	derivative\:\sqrt{x-2}
integral from 0 to 1 of (3x+1)^{sqrt(2)}	\int\:_{0}^{1}(3x+1)^{\sqrt{2}}dx
derivative of f(x)=sqrt(8x+1)	derivative\:f(x)=\sqrt{8x+1}
inverse oflaplace (7s+10)/(7s^2+26s+25)	inverselaplace\:\frac{7s+10}{7s^{2}+26s+25}
f(x)=-tan(x)	f(x)=-\tan(x)
derivative of y=e^{4x^2}	derivative\:y=e^{4x^{2}}
integral from-2 to 3 of (30)/(x^4)	\int\:_{-2}^{3}\frac{30}{x^{4}}dx
integral of-y/(z^2)	\int\:-\frac{y}{z^{2}}dz
integral of (10)/((t^2+1)^{3/2)}	\int\:\frac{10}{(t^{2}+1)^{\frac{3}{2}}}dt
integral of 1/((x-5)^2)	\int\:\frac{1}{(x-5)^{2}}dx
(sinh(x))^'	(\sinh(x))^{\prime\:}
integral of 6sin(3x)ln(sin(3x))	\int\:6\sin(3x)\ln(\sin(3x))dx
25y^{''}-30y^'+9y=0	25y^{\prime\:\prime\:}-30y^{\prime\:}+9y=0
integral of 1/(2t^2+3t+1)	\int\:\frac{1}{2t^{2}+3t+1}dt
derivative of ({r}(x)/x)	\frac{d}{dx}(\frac{{r}(x)}{x})
integral from 1 to 3 of (3x+2)^2	\int\:_{1}^{3}(3x+2)^{2}dx
(\partial)/(\partial x)(x/(3+6x^2+7y^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{3+6x^{2}+7y^{2}})
derivative of arcsin(xy)	\frac{d}{dx}(\arcsin(xy))
f(x)=(xe^x)/(x+e^x)	f(x)=\frac{xe^{x}}{x+e^{x}}
integral of 4/((x+2)(x-2))	\int\:\frac{4}{(x+2)(x-2)}dx
integral from 0 to 1 of (x-1)/(x^2+3x+2)	\int\:_{0}^{1}\frac{x-1}{x^{2}+3x+2}dx
tangent of f(x)=(e^x)/x ,\at x=1	tangent\:f(x)=\frac{e^{x}}{x},\at\:x=1
derivative of sqrt((3x+2/(5-4x)))	\frac{d}{dx}(\sqrt{\frac{3x+2}{5-4x}})
(\partial)/(\partial x)(1/(ln(y/x)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\ln(\frac{y}{x})})
simplify ln(((x+6)^4e^{5x^3-3})/(x+2x^3))	simplify\:\ln(\frac{(x+6)^{4}e^{5x^{3}-3}}{x+2x^{3}})
derivative of ln(y^2)	derivative\:\ln(y^{2})
simplify 7/4 x^4-6/5 x^3	simplify\:\frac{7}{4}x^{4}-\frac{6}{5}x^{3}
limit as x approaches 0 of (e^x-1)/(17x)	\lim\:_{x\to\:0}(\frac{e^{x}-1}{17x})
derivative of f(x)=3^x-5e^x	derivative\:f(x)=3^{x}-5e^{x}
integral of 9xe^{(-3x)}	\int\:9xe^{(-3x)}dx
integral of d	\int\:ddd
inverse oflaplace 1/(4s^2+1)	inverselaplace\:\frac{1}{4s^{2}+1}
integral of cos(1/2)x	\int\:\cos(\frac{1}{2})xdx
derivative of ln(2x^4-x^3+3x^2-3x)	\frac{d}{dx}(\ln(2x^{4}-x^{3}+3x^{2}-3x))
implicit (dy)/(dx),x^3y^5+3x=8y^3+1	implicit\:\frac{dy}{dx},x^{3}y^{5}+3x=8y^{3}+1
integral from 0 to 4 of sqrt(1+e^{-2y)}	\int\:_{0}^{4}\sqrt{1+e^{-2y}}dy
integral of (28s+28)/((s^2+1)(s-1)^3)	\int\:\frac{28s+28}{(s^{2}+1)(s-1)^{3}}ds
(\partial)/(\partial x)(3x+4y^2+3x^2y^3)	\frac{\partial\:}{\partial\:x}(3x+4y^{2}+3x^{2}y^{3})
integral of x-2pi	\int\:x-2πdx
integral of (x) 3/4 x^2-4x+8	\int\:(x)\frac{3}{4}x^{2}-4x+8dx
derivative of (2x^3(4x^2))	\frac{d}{dx}((2x^{3})(4x^{2}))
slope ofintercept (0,5),(-1.5,1)	slopeintercept\:(0,5),(-1.5,1)
2t(dy)/(dt)-4y=sqrt(t)	2t\frac{dy}{dt}-4y=\sqrt{t}
sum from n=1 to infinity of 1/(4^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{4^{n}}
laplacetransform (t^2-3t+2)sin(3t)	laplacetransform\:(t^{2}-3t+2)\sin(3t)
derivative of y=sin(9x)+cos(2x)	derivative\:y=\sin(9x)+\cos(2x)
derivative of 3arcsin(x/2)	\frac{d}{dx}(3\arcsin(\frac{x}{2}))
integral of 2sin(3x)	\int\:2\sin(3x)dx
y^{'''}-y^'=sin(x)	y^{\prime\:\prime\:\prime\:}-y^{\prime\:}=\sin(x)
(dy)/(dx)=((2x(y-1)))/(x^2+3)	\frac{dy}{dx}=\frac{(2x(y-1))}{x^{2}+3}
integral of 1/(x^2sqrt(16+x^2))	\int\:\frac{1}{x^{2}\sqrt{16+x^{2}}}dx
taylor-1/(x^2),2	taylor\:-\frac{1}{x^{2}},2
inverse oflaplace (5s)/(12s^2+5s-2)	inverselaplace\:\frac{5s}{12s^{2}+5s-2}
integral of 2e^{-0.1x}	\int\:2e^{-0.1x}dx
integral of 5sin(6pit)	\int\:5\sin(6πt)dt
integral of xcos(7pix^2)	\int\:x\cos(7πx^{2})dx
(dy)/(dx)=x^6y^{-3}	\frac{dy}{dx}=x^{6}y^{-3}
t^2(dy)/(dt)-t=1+y+ty,y(1)=5	t^{2}\frac{dy}{dt}-t=1+y+ty,y(1)=5
integral of 24arctan(sqrt(x))	\int\:24\arctan(\sqrt{x})dx

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